- #1
mjordan2nd
- 177
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Homework Statement
Prove [tex]\nabla \bullet E =4 \pi \rho[/tex] from [tex]\partial_{\beta}F^{\alpha \beta}=4 \pi J^{\alpha}[/tex] where [tex]J^{\alpha}=(\rho, J^{1}, J^{2}, J^{3})[/tex].
Homework Equations
We are given that [tex]F_{\alpha \beta}[/tex] is
0~~~~E_x~~~E_y~~~E_z
-E_x~~~0~~~~-B_z~~B_y
-E_y~~B_z~~~~0~~~-B_x
-E_z~~-B_y~~~B_x~~~0
(Sorry, don't know how to do matrices.)
Raising the indices I should get
0~~~-E_x~~-E_y~~-E_z
E_x~~~0~~~~-B_z~~B_y
E_y~~B_z~~~~0~~~-B_x
E_z~~-B_y~~~B_x~~~0
The Attempt at a Solution
[tex]\partial_{\beta}F^{\alpha \beta}=4 \pi J^{\alpha}=>-\partial_{i}F^{0i}=\rho=-\partial_{i}E_{i}[/tex]. I don't know why I keep getting that pesky negative sign! Can anyone point me in the right direction?